The
Tusi-couple is a
mathematical device in which a small
circle rotates inside a larger circle twice the
diameter of the smaller circle. Rotations of the circles cause a point on the
circumference of the smaller circle to
oscillate back and forth in
linear motion along a diameter of the larger circle.
It was developed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi as an alternative to the problematic equant introduced over a thousand years earlier in Ptolemy's Almagest.
Original description
Some modern commentators also call the Tusi couple a "rolling device" and describe it as a small circle
rolling inside a large fixed circle. However, Tusi himself described it differently:
:if two coplanar circles, the diameter of one of which is equal to half the diameter of the other, are taken to be internally tangent at a point, and if a point is taken on the smaller circle—and let it be at the point of tangency—and if the two circles move with simple motions in opposite direction in such a way that the motion of the smaller [circle] is twice that of the larger so the smaller completes two rotations for each rotation of the larger, then that point will be seen to move on the diameter of the larger circle that initially passes through the point of tangency, oscillating between the endpoints.
Other sources
The term "Tusi couple" is a modern one, coined by Edward Kennedy in 1966. It is one of several late Islamic astronomical devices bearing a striking similarity to models in
De revolutionibus orbium coelestium, including his
Mercury model and his theory of
trepidation. Historians suspect that Copernicus or another European author had access to an Islamic astronomical text, but an exact chain of transmission has not yet been identified, although the 16th century scientist and traveler
Guillaume Postel has been suggested.
There are other sources for this mathematical model for converting circular motions to reciprocating linear motion. It is found in Proclus's Commentary on the First Book of Euclid and the concept was known in Paris by the middle of the 14th Century. In his questiones on the Sphere (written before 1362), Nicole Oresme described how to combine circular motions to produce a reciprocating linear motion. Oresme's description is unclear and it is not certain whether this represents an independent invention or an attempt to come to grips with a poorly understood Arabic text.
Since the Tusi-couple was used by Nicolaus Copernicus in his reformulation of mathematical astronomy, there is a growing consensus that he became aware of this idea in some way. It has been suggested both by a historian of Medieval European astronomy and by a historian of Arabic astronomy that the idea of the Tusi couple may have arrived in Europe leaving few manuscript traces, since it could have occurred without the translation of any Arabic text into Latin. One possible route of transmission may have been through Byzantine science, which translated some of al-Tusi's works from Arabic into Byzantine Greek. Several Byzantine Greek manuscripts containing the Tusi-couple are still extant in Italy.
Notes
References
Di Bono, Mario. "Copernicus, Amico, Fracastoro and Tusi's Device: Observations on the Use and Transmission of a Model." Journal for the History of Astronomy 26 (1995):133-154.
Kennedy, E. S. "Late Medieval Planetary Theory." Isis 57 (1966):365-378.
Kren, Claudia. "The Rolling Device of Naṣir al-Dīn al-Ṭūsī in the De spera of Nicole Oresme." Isis 62 (1971): 490-498.
Ragep, F. J. "The Two Versions of the Tusi Couple," in From Deferent to Equant: A Volume of Studies in the History of Science in Ancient and Medieval Near East in Honor of E. S. Kennedy, ed. David King and George Saliba, Annals of the New York Academy of Sciences, 500. New York Academy of Sciences, 1987. ISBN 0-89766-396-9 (pbk.)
Ragep, F. J. Nasir al-Din al-Tusi's "Memoir on Astronomy," Sources in the History of Mathematics and Physical Sciences,12. 2 vols. Berlin/New York: Springer, 1993. ISBN 3-540-94051-0 / ISBN 0-387-94051-0.
External links
Dennis W. Duke, Ancient Planetary Model Animations includes two links of interest:
* An interactive Tusi couple
* Arabic models for replacing the equant
George Saliba, "Whose Science is Arabic Science in Renaissance Europe?" Discusses the model of Nasir al-Din al-Tusi and the interactions of Arabic, Greek, and Latin astronomers.
Category:Islamic astronomy
